Lorentz Group in Optical Sciences

Squeezed States!

The picture is for Lorentz-boosted extended objects in particle physics. The supporting mathematics is called the Lorentz group. This group, by now, is the standard mathematical device for quantum and classical optics.
It is by now widely established that the Wigner function is the key scientific language for quantum optics, but not many people know that those Wigner functions in optics also serve as the representation of the Lorentz groups, such as O(2,1) and O(3,2) which are the fundamental languages for the one- and two-mode squeezed states. When you do squeezed states, you are doing the Lorentz groups.

On this subject, with Marilyn Noz, I have written a book entitled Phase Space Picture of Quantum Mechanics.

Recently, I have been publishing papers on applications of the Lorentz group to classical ray optics, mostly in Phys. Rev. E. Those papers were also archived in Los Alamos. Some of them are listed below.

My youngest co-authors! Sibel Baskal Elena Georgeiva.

• Jones matrix formalism as a representation of the Lorentz group ArXiv , published in J. Opt. Soc. Am. A /Vol.14, No.9 page 2290 (1997).

• Stokes parameters as a Minkowskian four-vector ArXiv
  Physical Review E

• Wigner rotations and Iwasawa decompositions in polarization optics ArXiv
  Physical Review E

• Interferometers and decoherence matrices ArXiv
  Physical Review E

• Iwasawa effect in multilayer optics ArXiv
  Physical Review E

• Wigner rotations in laser cavities ArXiv
  Physical Review E

• Three-lenses at most in multi-lens system ArXiv
  Physical Review E

• Optics computers for space-time symmetries ArXiv
  presented at various conferences during the year 1999.

• Lens optics and group contractions ArXiv
  Physical Review E

• Cyclic representations of multilayer optics ArXiv
  Physical Review E

• Physics of two-by-two matrices ArXiv
  presented at various conferences during the year 2003.

• Lorentz group in ray optics (Review Paper) AriXiv
  Journal of Optics B